Problem: Nadia is 40 years older than William. For the last 3 years, Nadia and William have been going to the same school. Seventeen years ago, Nadia was 5 times as old as William. How old is Nadia now?
Answer: We can use the given information to write down two equations that describe the ages of Nadia and William. Let Nadia's current age be $n$ and William's current age be $w$ The information in the first sentence can be expressed in the following equation: $n = w + 40$ Seventeen years ago, Nadia was $n - 17$ years old, and William was $w - 17$ years old. The information in the second sentence can be expressed in the following equation: $n - 17 = 5(w - 17)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $n$ , it might be easiest to solve our first equation for $w$ and substitute it into our second equation. Solving our first equation for $w$ , we get: $w = n - 40$ . Substituting this into our second equation, we get the equation: $n - 17 = 5($ $(n - 40)$ $ -$ $ 17)$ which combines the information about $n$ from both of our original equations. Simplifying the right side of this equation, we get: $n - 17 = 5n - 285$ Solving for $n$ , we get: $4 n = 268$ $n = 67$.